Average Error: 0.0 → 0.0
Time: 8.1s
Precision: 64
\[x \cdot x + y \cdot y\]
↓
\[\mathsf{fma}\left(x, x, y \cdot y\right)\]
x \cdot x + y \cdot y
↓
\mathsf{fma}\left(x, x, y \cdot y\right)
double f(double x, double y) {
        double r119357 = x;
        double r119358 = r119357 * r119357;
        double r119359 = y;
        double r119360 = r119359 * r119359;
        double r119361 = r119358 + r119360;
        return r119361;
}
↓
double f(double x, double y) {
        double r119362 = x;
        double r119363 = y;
        double r119364 = r119363 * r119363;
        double r119365 = fma(r119362, r119362, r119364);
        return r119365;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot x + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, y \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, y \cdot y\right)\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))